Splitting schemes and unfitted mesh methods for the coupling of an incompressible fluid with a thin-walled structure

Miguel Angel Fernández 1, * Mikel Landajuela 2
* Corresponding author
1 COMMEDIA - COmputational Mathematics for bio-MEDIcal Applications
Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 REO - Numerical simulation of biological flows
SU - Sorbonne Université, Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
Abstract : Two unfitted mesh methods for a linear incompressible fluid/thin-walled structure interaction problem are introduced and analyzed. The spatial discretization is based on different variants of Nitsche's method with cut elements. The degree of fluid-solid splitting (semi-implicit or explicit) is given by the order in which the space and time discretizations are performed.The a priori stability and error analysis shows that strong coupling is avoided without compromising stability and accuracy. Numerical experiments in a benchmark illustrate the accuracy of the different methods proposed.
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Miguel Angel Fernández, Mikel Landajuela. Splitting schemes and unfitted mesh methods for the coupling of an incompressible fluid with a thin-walled structure. IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2019, ⟨10.1093/imanum/dry098⟩. ⟨hal-01309462v2⟩

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